Tim,
That's quite a wide range of hunting options you mentioned.
Just to once more point out the obvious (hey, I'm good for something!)...
Brown/Grizzly Bears, Dall Sheep, and Mountain Goat require guides for non-resident hunters. It's a lame law, I know. As many "lower 48" hunters have more experience than the average Alaskan local.
When considering a "Guided Hunt", remember your looking at approx $10,000 for Brown Bear and Sheep, maybe less for Mt Goats.
A "do-it-yourself" hunt for Caribou and Black Bear is a good option. I don't know a lot about those hunts though. Lilbiggun post here from time to time, he speaks well of an outfitter from Soldatna.
A Fall Black Bear/Blacktail Deer hunt in S.E. Alaska is probably the most affordable hunt going these days. If you have a varmint caller, you may even get a chance at a wolf.
The obvious choice is to hire an outfitter who hunts from a boat. That should include some good halibut and crabbing oppurtunities. Another thought is to bring a truck with a camper (or well set up "topper" with big tent) and get on the Alaska Marine Highway Ferry out of Bellingham Wa. Take the ferry to Ketchikan, get off, then catch another ferry to Prince of Wales Island (yes, that's part of the U.S.) and hunt the extensive road system for Black Bears and Blacktails.
You'll experience a "mini-cruise" up part of the Inside Passage (the ferry's have basic cabins) and get to hunt some awesome country!
Just some thoughts...